A Fast Algorithm for Euler's Elastica Minimization problems and some new developments with continuous max-flow algorithms
Minimization of functionals related to Euler's elastica energy has a wide range of applications in computer vision and image processing. A high order nonlinear partial differential equation (PDE) needs to be solved, and the gradient descent method usually takes high computational cost. In this paper, we propose a fast and efficient numerical algorithm to solve minimization problems related to Euler's elastica energy and show applications to variational image denoising, image inpainting, and image zooming. We reformulate the minimization problem as a constrained minimization problem, followed by an operator splitting method and relaxation. Fast numerical schemes were proposed for the proposed constrained minimization problem.
Numerical tests on real and synthetic cases are supplied to demonstrate the efficiency of our method.
The technique can be extended to a number of other applications related to curvature minimization. In the end, we shall also show the essential ideas to use these techniques for applications that have replace the "length" regularization" by "curvature" regularizations.
In the end, I will also talk about some of new developments related to graph cut, convex relaxation and continuous max-flow algorithms. These algorithms offer new fast and robust approaches for segmentation and classification problems for image processing and computer vision.
Prof Tai Xue-Cheng is a member of the Department of Mathematics atthe University of Bergen of Norway. His research interests include Numerical PDEs, optimization techniques, inverse problems, and image processing. He has done significant research work his research areas and published a large number of top quality international conference and journal papers. He is the winner of the 8th Feng Kang Prize for scientific computing. He served as organizing and program committee members for a number of international conferences and has been ofteninvited for international conferences. He has served as referee and reviewers for many premier conferences and journals. Dr. Tai is a member of the editor board for 6 international journals.